The former manager of a Chase bank branch in The Bronx yesterday tearfully pleaded guilty in a $3 million-plus scam involving bogus income-tax refunds.

Katherine Torres (pictured), 52, admitted that she authorized tellers to cash “tens of thousands of dollars” worth of refund checks brought in “on a near-daily basis” by an alleged fraudster in 2006 and ’07.

Torres, who faces nearly four years behind bars under a plea bargain, broke down as the judge discussed her potential sentence.

The Manhattan US Attorney’s Office said the refunds were obtained by filing phony tax returns using identities stolen from Puerto Rican residents, who are generally exempt from paying federal income tax and don’t have to file.

Ex-Chase employees Rosalind Smith, 41, and Judith Fulgencio, 32, also pleaded guilty. Chase said the three women were fired in 2007.